观察下列等式1/(1*2)=1-1/2 1/(2*3)=1/2-1/3 1/(3*4)=1/3-1/4将以上三个灯市两边分别相加得:1/(1*2)+1/(2*3)+1/(3*4)=1-1/2+1/2-1/3+1/3-1/4=1-1/4=3/41.猜想并写出:1/[n(n+1)]=?2.直接写出下列各试的计算结果:(1)1/(1*2)+1/(2*3
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![观察下列等式1/(1*2)=1-1/2 1/(2*3)=1/2-1/3 1/(3*4)=1/3-1/4将以上三个灯市两边分别相加得:1/(1*2)+1/(2*3)+1/(3*4)=1-1/2+1/2-1/3+1/3-1/4=1-1/4=3/41.猜想并写出:1/[n(n+1)]=?2.直接写出下列各试的计算结果:(1)1/(1*2)+1/(2*3](/uploads/image/z/5227920-0-0.jpg?t=%E8%A7%82%E5%AF%9F%E4%B8%8B%E5%88%97%E7%AD%89%E5%BC%8F1%2F%281%2A2%29%3D1-1%2F2+1%2F%282%2A3%29%3D1%2F2-1%2F3+1%2F%283%2A4%29%3D1%2F3-1%2F4%E5%B0%86%E4%BB%A5%E4%B8%8A%E4%B8%89%E4%B8%AA%E7%81%AF%E5%B8%82%E4%B8%A4%E8%BE%B9%E5%88%86%E5%88%AB%E7%9B%B8%E5%8A%A0%E5%BE%97%3A1%2F%281%2A2%29%2B1%2F%282%2A3%29%2B1%2F%283%2A4%29%3D1-1%2F2%2B1%2F2-1%2F3%2B1%2F3-1%2F4%3D1-1%2F4%3D3%2F41.%E7%8C%9C%E6%83%B3%E5%B9%B6%E5%86%99%E5%87%BA%3A1%2F%5Bn%28n%2B1%29%5D%3D%3F2.%E7%9B%B4%E6%8E%A5%E5%86%99%E5%87%BA%E4%B8%8B%E5%88%97%E5%90%84%E8%AF%95%E7%9A%84%E8%AE%A1%E7%AE%97%E7%BB%93%E6%9E%9C%3A%281%291%2F%281%2A2%29%2B1%2F%282%2A3)
观察下列等式1/(1*2)=1-1/2 1/(2*3)=1/2-1/3 1/(3*4)=1/3-1/4将以上三个灯市两边分别相加得:1/(1*2)+1/(2*3)+1/(3*4)=1-1/2+1/2-1/3+1/3-1/4=1-1/4=3/41.猜想并写出:1/[n(n+1)]=?2.直接写出下列各试的计算结果:(1)1/(1*2)+1/(2*3
观察下列等式
1/(1*2)=1-1/2 1/(2*3)=1/2-1/3 1/(3*4)=1/3-1/4
将以上三个灯市两边分别相加得:
1/(1*2)+1/(2*3)+1/(3*4)=1-1/2+1/2-1/3+1/3-1/4=1-1/4=3/4
1.猜想并写出:1/[n(n+1)]=?
2.直接写出下列各试的计算结果:
(1)1/(1*2)+1/(2*3)+1/(3*4)+...+1/(2006*2007)=?
(2)1/(1*2)+1/(2*3)+1/(3*4)+...+1/[n(n+1)]=?
要有解题思路 答案我已经有
1.n-1/(n+1)
2.(1)2006/2007 (2)n/(n+1)
没有一个全对的 太令我失望鸟....
书的答案是这样的
观察下列等式1/(1*2)=1-1/2 1/(2*3)=1/2-1/3 1/(3*4)=1/3-1/4将以上三个灯市两边分别相加得:1/(1*2)+1/(2*3)+1/(3*4)=1-1/2+1/2-1/3+1/3-1/4=1-1/4=3/41.猜想并写出:1/[n(n+1)]=?2.直接写出下列各试的计算结果:(1)1/(1*2)+1/(2*3
你的1题答案肯定错了!
因为:
1/[n(n+1)]=(n+1-n)/[n(n+1)]
=(n+1)/[n(n+1)]-n/[n(n+1)]
=1/n-1/(n+1)
这个当公式代入2题
(1)1/(1*2)+1/(2*3)+1/(3*4)+...+1/(2006*2007)
=1-1/2 +1/2-1/3 +1/3 -1/4 ...+1/2006-1/2007
=1-1/2007
=2006/2007
(2)同理
1/(1*2)+1/(2*3)+1/(3*4)+...+1/[n(n+1)]
=1-1/(n+1)
=n/(n+1)
1/[n(n+1)]=1/n-1/(n+1)
1/(1*2)+1/(2*3)+1/(3*4)+...+1/(2006*2007)
=(1/1-1/2)+(1/2-1/3)+……+(1/2006-1/2007)
=1-1/2007
=2006/2007
(2)1/(1*2)+1/(2*3)+1/(3*4)+...+1/[n(n+1)]
=(1/1-1/2)+(1/2-1/3)+……+[1/n-1/(n+1)]
=1-1/(n+1)
=n/(n+1)
1. 1/n-1/(n+1)
2. (1) =1-1/2+1/2-1/3+1/3-1/4+……+1/2006-1/2007=1-1/2007=2006/2007
(2) =1-1/2+1/2-1/3+1/3-1/4+……+1/n-1/(n+1)=1-1/(n+1)=n/(n+1)
自己错了还怪别人,脑袋被门夹了。。。
1.
1/[n(n+1)]=1/n-1/(n+1)
2.
(1) 1/(1*2)+1/(2*3)+1/(3*4)+...+1/(2006*2007)
=1-1/2 +1/2-1/3 +1/3 -1/4 ...+1/2006-1/2007
相邻2项一正一负,都消掉了
=1-1/2007
=2006/2007
(2)1/(1*2)+1/(2*3)+1/(3*4)+...+1/[n(n+1)]
=1-1/2 +1/2-1/3 +1/3 -1/4 ...+1/n-1/(n+1)
=1-1/(n+1)
=n/(n+1)
要拆项
1/(1*2)=1-1/2
1/(2*3)=1/2-1/3
1/(3*4)=1/3-1/4
.....
1/(n*(n+1))=1/n-1/(n+1)
连续消去即可得到结果
1.:1/n-1/(n+1)
2(1):原试=1-1/2+1/2-1/3+1/3-1/4...+1/2006-1/2007
=1-1/2007
=2006/2007
(2)同理=1-1/(n+1)
=n/(n+1)
我对了啊!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
有了你还问